The original mass spectrometry search engines used simple algorithms for peptide identification. Recent tools improved accuracy by adding several extra components such as fragment ion intensities or retention times prediction and training target-decoy classifiers on-the-fly, leading to sometimes inconsistent results. Our study explores the impact of replacing those extra components with a deep-learning pretrained model that directly learns the complex relationship between the full spectra and associated peptide sequence, without using decoys. This simplified workflow has fewer parameters to tweak, making it easier to use and perform robustly on data from instruments and use-cases never seen during training. Surprisingly, our approach consistently identifies more peptides than FragPipe, PEAKS, and Proteome Discoverer (12%, 9%, and 21% more, respectively, across a range of datasets). Tesorai Search is also fast - 250 immunopeptidomics searches in 45 minutes - and free for academics, available as a webserver at console.tesorai.com.